I have no desire to spend hundreds of dollars on this specialized equipment to make sausage, which I may only use a few times a year.
There must be some other alternatives!
edit: no Kitchen Aid mixer (yes I know it makes this even more difficult)
Well, you don't need to spend hundreds of dollars, but you might need to put in more elbow grease. You can get a hand-crank meat grinder for about $30 or so and a manual sausage stuffer for about the same. You could save on the grinder if you have a food processor or blender that can have its way with the meat.
Do you have a KitchenAid stand mixer? If so, I'd suggest getting these attachments: KitchenAid FGA Food Grinder Attachment for Stand Mixers and KitchenAid SSA Sausage Stuffer Kit Attachment for Food Grinder. They're under $50 combined, and small enough to fit in a deep drawer or cabinet.
If you're good with the knife work, you can just dice up everything super fine for sausage, but it won't taste as good; you're going to have some temperature control issues when whipping it as well.
I'd second the suggestions to buy a used grinder or a kitchen aid and attachment (Seriously, the kitchen aid is a must have. You'll use it all the time.)
You can buy different ingredients depending on how much effort you are willing to put in:
Many places will do premade sausagemeat which you can but into casing yourself (you could add your own seasonings to this meat).
A good butcher will grind meat for you - I'm sure they would even advise you on the proportions of particular meat (I would use pork belly and shoulder with maybe a little extra fat in) and you could probably even get them to use different meats too (beef?).
One method i've seen (but not personally tried) is using a piping bag with the casing on the end to squeeze the sausage meat into the casing, you'd need to tie it every now and then (unless you wanted giant sausage of course :D )
Well if you want to go totally old school you go out and buy some cull fat. It's the membrane that holds the insides together. Your local butcher can get you some.
Get your meats and fat then start chopping like crazy to make it as small a dice as possible. (Or go to your local butcher and ask him/her to grind it for you. It won't cost much.) Mix in your spices and such until it's what you want. You know, follow your favourite recipe.
Start making patties/logs/egg-shapped mounds/whatever shape you like of meat and wrap them in the cull fat.
A nice addition is putting a bay leaf inside each wrap.
To cook, you brown them off and either braise them off like a few traditional British dishes (which have a name which isn't very PC) or just toss them into the oven and roast them off.
There you have it. A minced meat like sausage that can be made without the use of modern gadgits.
Mind you there is alot to be said about those cheap $25 hand grinders!